The authorites are still keeping the eight rescued boys away from their parents for fear of infection.
Boys from the soccer team trapped inside Tham Luang cave covered in hypothermia blankets react to the camera in Chiang Rai, Thailand, in this still image taken from a July 3, 2018 video by Thai Navy Seal.
Tuesday's operation began just after 10 a.m.
A health official earlier described the mental and physical condition of the eight rescued so far as "good", adding they will be kept in hospital for around a week. Another two more boys left the cave complex a short time later followed by the fourth boy.
On Tuesday, the four children and their 25-year-old soccer coach still in the cave, rescue mission head Narongsak Osotthanakorn told reporters Musk's submarine was appreciated but not practical.
Four boys were rescued on Monday, joining the first four boys who were extracted Sunday evening in the hospital. They began again at 11 am on Monday after the teams had stopped for the night to rest and to replenish equipment and oxygen supplies.More news: George Clooney reported hurt in motorcycle crash in Italy
Mr Narongnsak said this phase may take longer than the previous two rescue missions.
The "Wild Boars" soccer team and their coach got trapped on June 23 when they set out to explore the vast cave complex after soccer practice, when a rainy season downpour flooded the tunnels.
The complex rescue mission to extract the football team has been ongoing for several days, with an global team of rescue divers leading each boy individually out of the cave complex, fitted with a full-face scuba mask and carrying a supply of oxygen so they can pass through kilometers of tapering tunnels flooded with monsoon rains.
Since the operation started, the area outside the cave's entrance has filled with media, volunteers and onlookers.
A Thai well wisher puts a poster to pray for boys and their football coach.
"Doctors have treated the boys and now all of them are okay and cheerful".More news: China: Liu Xia free and on her way to Germany
The eccentric inventor had hoped the sub - built from spare rocket parts and named Wild Board after the stranded children's soccer team - could be used in the rescue.
"We were obviously very afraid of any kind of panic from the divers", he said, adding he was in awe of the boys' ability to stay calm.
A spokesperson from the Thai public health authority said that they were in "high spirits" and also claimed that as they are football players, they have high immune systems.
"They are diving in something considered (an) extremely hazardous environment in zero visibility, the only light that is in there is the torch light we bring our self".
At least nine ambulances and a convoy of other vehicles were at the cave site Tuesday.
People across Thailand cheered the rescue operation, including at the Mae Sai Prasitsart school where six of the trapped boys are students. The first and longest mission took 11 hours.More news: WhatsApp suggests ways to combat fake news
All 12 boys and their football coach trapped in Tham Luang cave for 17 days have been safely rescued.
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